[geometry-ml:05741] Dominik Inauenさんの講演

[Takashi Tsuboi]

トポロジーML、ジオメトリーML,力学系MLの皆様
クロスポストをご容赦ください。

Dominik Inauen (University of Leipzig)さんが来日され、
"Rigidity and Flexibility of Isometric Embeddings"
という題目で、6月20日（木）東京大学大学院数理科学研究科で、
7月16日（火）京都大学理学部数学教室で講演されます。
来場いただければ幸いです。
なお、6月20日（木）のトポロジー火曜セミナーは、
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
のトップでの参加登録が必要です。
7月16日（火）のセミナー　https://www.math.kyoto-u.ac.jp/ja/event/seminar/5398
に引き続き、7月17日（水）にも研究セミナーを予定しています。
坪井　俊 (RIKEN iTHEMS)
===
Speaker: Dominik Inauen (University of Leipzig)

Title of Talk: Rigidity and Flexibility of Isometric Embeddings

Abstract: The problem of embedding abstract Riemannian manifolds 
isometrically (i.e. preserving the lengths) into Euclidean space stems 
from the conceptually fundamental question of whether abstract 
Riemannian manifolds and submanifolds of Euclidean space are the same. 
As it turns out, such embeddings have a drastically different behaviour 
at low regularity (i.e. C^1) than at high regularity (i.e. C^2). For 
example, by the famous Nash--Kuiper theorem it is possible to find C1 
isometric embeddings of the standard 2-sphere into arbitrarily small 
balls in R^3, and yet, in the C^2 category there is (up to translation 
and rotation) just one isometric embedding, namely the standard 
inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one 
might ask if there is a sharp regularity threshold in the Holder scale 
which distinguishes these flexible and rigid behaviours. In my talk I 
will review some known results and argue why the Holder exponent 1/2 can 
be seen as a critical exponent in the problem.